-LRB- CNN -RRB- -- Negotiators for Iran and six world powers completed the first day of discussions on Iran 's nuclear program Monday in Moscow .

This third round of talks , called after two previous rounds of discussions yielded little result , was marked by `` serious and constructive '' discussions , Iran 's semi-official FARS News Agency quoted Deputy Chief Negotiator Ali Baqeri as saying .

An EU official described the meeting as an `` intense and tough exchange of views . ''

Western powers fear that Iran may be trying to build nuclear weapons , despite its insistence that its nuclear program is for peaceful purposes . The West has been using sanctions and diplomacy to try to stop Iran from producing nuclear arms .

The EU official , who was not authorized to speak to the media due to the sensitivity of the talks , said Iran responded to proposals brought up at the last round of talks in Baghdad , `` but , in doing so , brought up lots of questions and well-known positions , including past grievances . ''

Iran rejected calls during earlier talks for it not to enrich uranium to the point that it can be used for weapons , while the international powers refused Tehran 's demand for an immediate end to sanctions weighing on its economy .

Iran 's leaders also continued to take a firm line outside of the negotiations . On Monday , Iranian Supreme Leader Ayatollah Ali Khamenei said the country has been the object of `` non-stop conspiracies of all the world powers . ''

`` But the efforts of all the hegemonic powers to push the Iranian nation out of the scene will definitely and surely remain futile again this time , '' he said .

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If the negotiations in Moscow unravel , the potential consequences for the Middle East and the rest of the world could be grave . Israel , which is believed to have its own nuclear arsenal and is alarmed over Tehran 's hostility toward the Jewish state , has said it may attack Iran to try to stop Tehran from developing nuclear weapons .

And Iran 's strategic position near crucial oil shipping routes means the escalation of tensions could put further pressure on the fragile global economy .

After the previous round of negotiations in Baghdad last month , which ran beyond the original schedule , EU foreign policy chief Catherine Ashton offered a glimmer of hope for the Moscow talks . `` It 's clear that we both want to make progress , '' she said at the time .

Iran 's top negotiator , Saeed Jalili , struck a nuanced position after the Baghdad talks , asserting Iran 's right to pursue peaceful nuclear energy but also saying that progress had been made during the meeting .

Sanctions imposed on Iran by the United Nations , the United States and the European Union were one of the key stumbling blocks .

The sanctions appear to be inflicting considerable damage on the Iranian economy . And because 80 % of Iran 's foreign revenues are derived from oil exports , an embargo by the EU set to go into effect in July will add further pressure .

Jalili said that the removal of `` hostile measures '' would increase cooperation .

`` The current strategy of pressure could make the talks come to an end , '' he warned . Iran has previously threatened to close the Strait of Hormuz , a vital oil shipping lane , over the sanctions issue .

But U.S. Secretary of State Hillary Clinton insisted the sanctions will remain in place .

`` Iran now has the choice to make , '' she said . `` Will it meet its international obligations and give the world confidence about its intentions , or not . ''

The six world powers made Iran an offer for stopping its processing of medium-enriched uranium , EU officials said .

The proposal also called for Tehran to prove its nuclear program is being used for peaceful purposes as it claims , and comply with U.N. Security Council resolutions , according to a Western official , who spoke on condition of anonymity because of the sensitivity of the discussions .

Iran 's counterproposal included five areas of nuclear and non-nuclear cooperation , according to the state-run Islamic Republic News Agency .

Adding to the complexity of the situation , a U.N. report released just after the Baghdad talks said that inspectors had found a high level of enriched uranium in Iran .

The U.N. 's International Atomic Energy Agency asked Iran to explain the presence of particles of enrichment levels of up to 27 % , found in an analysis of environmental samples taken in February at the Fordo fuel enrichment plant near the city of Qom .

The previous highest level had been 20 % , typically used for hospital isotopes and research reactors , but is also seen as a shortcut toward the 90 % enrichment required to build nuclear weapons .

Iran said in response that the production of such particles `` above the target value '' may happen for `` technical reasons beyond the operator 's control . ''

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CNN 's Elise Labott contributed to this report .

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NEW : EU official describes meeting as `` intense and tough exchange of views

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Differences remain between the sides after talks last month in Baghdad

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Western nations suspect Iran wants to build nuclear weapons , an assertion Tehran denies

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Israel has threatened to attack Iran to stop it from developing nuclear weapons